THE SIZE-FREQUENCY DISTRIBUTION O F GRAINS O F SILVER HALIDE I N PHOTOGRAPHIC EMULSIONS AND ITS RE1,ATTON T O SENSTTOMETRIC C IIAR A CTERISTI CS * V. BY
SYSTER4ATIC CORRELATION
E. P. WIGHTMAN, A . P. H. TRIVELLT, A N D S. E. SHEPPARD
Introduction We have discussed, in previous papers,l the various methods used by others as well as by ourselves of obtaining the size-frequency distribution of the grains of a disperse system, and have given in detail, including the question of the errors involved, the principal method which we have employed in determining such distribution in the case of photographic emulsions. The sensitometric and size-frequency distribution characteristics of a number of commercial and of a few experimental emulsions were correlated as far as possible experimentally and a tentative general theory of the correlation was proposed, and given a preliminary test.? In the present paper we propose to consider a series of emulsions much more closely related to each other than those previously studied. They were a11 prepared in a similar manner with the exception of one factor which caused a change in the range of sizes of the grains, and hence in the size-frequency distribution.
* Communication No. 171 lrom the Research Laboratory of the Eastman Kodak Co. E. P. Wightman and S. E. Sheppard: Jour. Phys. Chem., 25, 181, 561 (1921); Brit. Jour. Phot., 68, 168 (1921); E . P. Wightman, A . P. H. Trivelli and S.E. Sheppard: Jour. Phys. Chem., 27, 141 (1923); Jour. Franklin Inst., 194, 485 (1922). E. P .Wightman, A . P. H. Trivclli and 5,E. Sheppard: Jour, Phys. Chem., 27, 141 (1923). ,
.
,
S i l i l c y HuEidc
iii
Pliotogyaphic Emdsiows
467
Bv producing these emulsions with extreme care it was possible not only to cause a gradual change in the size-frequency distribution, but likewise in the photographic properties, as will be seen later. In this connection a paper by M. Miyada,l which we had missed previously because of its inaccessibility, on the “Manufacture of Photographic Dry Plates,” should be mentioned. He prepared high-speed photographic dry-plates according to Eder’s ammoniacal method and studied various well known factors which influence the ripening and speed of the emulsion. The plates thus prepared gave a speed of about 13” Scheiner, i. e., approximately 130 H. and D. He examined the emulsions of these plates microscopically and showed that in general the faster the plate, the larger the grains in the emulsion, another experimental confirmation of the conclusions of ourselves and others on this question. Indeed, he prepared an emulsion by mixing various emulsions which differed in degree of ripening, and in size of grains. The emulsions thus prepared, contained much greater varieties of sizes of the grains, and gave a considerably higher speed ( 15O Scheiner, or about 230 H. and D.).
Experimental Part Each emulsion in the series, WGC, W7C, W8C, W9C, WlOC, W l l C , and W12C, was coated onto 12.7 X 17.78 cm2 (5 X i inch’) plates as in the case of ordinary photographic emulsions, except that the weight of the silver halide coated per unit area of plate was the same in every case. The photographic properties of these original coatings of the WGC, W9C, and W12C were carefully measured, i. e., speed, latitude and y, by the usual sensitometric methods employed in this Laboratory, and which need not be described here, except to say that for the exposures a Jones’ noninter-
‘
M. Miyada: Jour. Chem Ind. (Japan), 24, 884 (1921); Chem. Abst., 16, 2644 (1922). The sensitometric measurements were made by Mr. E. Huse, whom we wish to thank.
‘
408 E . P . Wightinan, A . P . H.Tiivelli avd
S.E . Sheppard
mittent sensitometer was used, and the densities were measured by means of a Martens' photometer, and that all density gamma, and other measurements were carefully checked.
TABLE I Photographic Properties of WC Series Emulsion _
_
_
Speed
~
.
-
-
W(iC W9C WISC
_ _
Latitude
?m
i.2
1"
(is
S.7
112
10.0
The resulting values are given in Table I , and are shown graphically in Fig. 1. I t is seen that in passing from W6C to W12C, i. e., from the smallest to the largest grained emulsion s
b ',
LATllUDt
SPlCU
--,I
;17/iI:; 8.0
-153
i.5-
-
ll.---40
-
1-
~
I
b
9 I L I T L
I1
Silver Halide in Photographic Emulsions
469
470 E . P . Wightman, '4.P. H . Trivelli and
S.E . Sheppard
Silver Halide in Photographic Enzuls.ions
471
the values of the total areas in each class-size, per cm2 of original plate surface, and also similar values for the one-grainlayer plates, from which the former values were derived.
Fig. 2
The curves for each emulsion are shown graphically in Figs. 2 t o 8 inclusive, and a photomicrograph of each, made a t X2500, is also appended; it is reduced by about one half in the reproduction. It is to be noted that in passing through
472 E. P. Wightman, A.P. H . Trivelli and S. E. Sheppard
Fig. 6
474 E . P . Wiglalunaiz, A . P. H . Trivelli a v d S. E. Sheppayd the series from W6C to W12C, the curves start with the exponential type y = yo
e-kx
(1)
and pass by gradations into a modified Gaussian form of error y = yo e-k(x--u)*
(2)
function and that the latter curves become broader and broader and flatter and flatter.
Fig. 8
This relation can also be seen by examining the parameters of these curves given in Table IV - yo and k decrease and a increases with the emulsion number throughout the series, which is the same as saying, with the increase of speed, since the latter (as seen above in Fig. 1) is a linear function of the former and has a positive slope. I n equation (l), yo represents the ordinate formed by the intersection of the curve with the y-axis, and k the degree of spread of the curve. I n (2), y c indicates the maximum ordinate, CY the position of this ordinate on the x-axis, and k has the same significance as in (1). Other important grain-characteristics of the emulsions are given in Table IV. The number of grains per cm? are ob-
Silver Halide in Photographic Emulsions
475
e .*
6
.-8 ti
00003dr!
c
000000r!
j:
0000000
6 Ir! r! r!
+ + + r!
Mm MmmMm
000Od00
I1
4’76 E . P.Wightman, A.P. H.. Trivelli and
S.E . Sheppard
tained by averaging the counts on a large number of photomicrograms from the one-grain-layer plates, taking into account the area of the photomicrograms, the area of the original plate and that of the one-layer plate, and the dilution fact0r.l Under the heading “Average Size Grain,” w signifies the weight of the average grain obtained by dividing the weight of silver halide per unit area of plate by the number of grains in that area. From the average weight is then obtained the average volume of the grain, in p 3 , by dividing it by the density of AgBr, 6.4’73, and applying the factor for converting cm3 to p 3 . We obtained the average projective area, from the frequency data by multiplying frequency per 1000 in each class by the average class size and dividing the sum of these by 1000. For comparison and for use in other calculations we consider the projective area as that of a circle‘equivalent to the actual projective area of the grain when planimetered. The average projective areas were obtained from both the observed and the calculated data. I) represents the average projective diameter of a grain, calculated from ;E. If we assume that the grains are spherical we may calculate from the diameter of the sphere, 7 ’ . On the other hand if we assume the grains to be plates instead of spheres, then dividing by 2 gives the thickness, ,; of the grains. If the grains were all spheres then 5 would equal ;’. But we know from microscopical and other evidence that there are manx plates as well as spherical grains, however, the largest ratio of width to thickness that we can get for the average grain is given in the column headed ;/E. Besides the average grain size, it is important to know the total projective areas of all the grains per unit area of the plate. I n the case of the original plate the grains of course are many layers deep and there must be considerable overlapping of the grains in one layer by those in the layer above
-
z,
c
1 For details of the whole process see Wightman, Trivelli and Sheppard: Jour. Phys. Chem., 27, 141 (1923).
Silver Halide in Photographic Emwlsions
477
it. To find just what this is for any given number of layers and the distribution of the overlap for the various sizes of grains is a very intricate problem not yet solved. It is all the more so when one considers that some of the overlapping grains lie in such intimate contact with those below that they form a clump which acts as a single unit towards the development action, and perhaps the light action also. We give in Table IV the total area of the grains on the original plate, without attempting t o analyse the data further. Similar figures are given for the one-grain-layer plate. There are two approximate methods of arriving at these data, either to multiply the number of grains per unit area of the plate by the average projective area, or by summing up the products of the frequencies by the average class size. The agreement in the two cases is seen i o be fairly good. The number of grains measured in obtaining the frequency data, the resolving power and turbidities' of the original emulsions, and the maximum grain size observed for each emulsion are likewise given in the table. The data in this table are plotted i n Figs. 9 and 10, all against the emulsion number (which, as stated above, may be replaced by the number representing the speed, y,, or latitude). It is seen from these graphs that the number of grains per cm2 of the original plate, and the parameters YO and k decrease regularly with increase of speed of the emulsion, and this decrease has almost the exponential form. The total area of grains on the original, however, decreases to a minimum and then slightly increases; and the resolving power of the original plates decreases for the first three emulsions and then remains constant for the others. All the other values plotted show a general increase with speed as might be expected except the
* F. E. Ross: Astrophys. Jour., 52, 201 (1920). These values were obtained for us by Dr. Ross whom we wish t o thank. For the resolving power t h e 30 mm fan test object was employed, using violet light and aesculin filter. Development was in MQ Process for 3 minutes a t 75. For turbidity white light a t violet focus was used, development also in MQ Process b u t for 3.5 minutes a t 70".
478 E . P. Wightvnan, A.P. H.Trivcl1.i and S. E. Sheppavd WC
SERIES
Fig. 9 yo =
A = X = total proj. area grains/cmt
= parameter
N = 0 = No. grains/cm2 orig. plate R.P. = A = resolving power
orig. plate = = parameter k = A = parameter OL
+
Fig. 10
0 = average w t . grains
W T
= =
A
= A = turbidity = c~= average area grain
X
6
= average thickness grains
-
D = A = average diam. grains Max. size = 0= max. size grain obs. V = x = average volume grain
Silver Halide in Photographic Emulsions
479
average thickness of the grains which passes through a maximum. The results so far obtained are for only one series of emulsions and of course should not be accepted as final. To make them of greater value it has been our intention to measure the various characteristics of several similar series in parallel and to take the average of them all. The present work also covers only the empirical relation of the grain to the Sensitometric characteristics of the original emulsions. I n another paper we hope to present the results of some work on single-layer plates prepared from such a series. It should be noted here likewise that work is in progress on a new series of emulsions which differ from the present series in that the frequency distribution of the slowest emulsions as well as the fastest can be represented entirely by exponential curves, the parameters yo and k , however, having a similar relation to each other as in the series above described.
Summary 1. A series of photographic emulsions has been prepared of which a correlation between the grain and sensitometric characteristics shows an apparently close relationship between the two. 2. These emulsions are strictly comparable because practically all the factors in their preparation were under control, only one being varied so as to progressively increase the speed of the emulsions in the series, and because equal weights of the emulsion containing in every case the same amount of silver halide by weight were coated on the plates. 3. ’ The equations which represent the grain-size-distribution of these emulsions show a steady transition from a steep exponential y = yo e-kn
to a flat, widely spread Gaussian type y = yo e--K(z--Ol)*.
,
480 E . P.lT,7ightnzoir, A.P.H.Trivelli aiid 5 . E . Slzeppnrd
That is to say, in passing through the series from the slow to the comparatively fast emulsion the parameters yo and k steadily decrease, while the parameter a , which is zero in the first two examples, then steadily increases. 4. Other grain characteristics were determined and they likewise showed the same progressive increase or decrease with the speed. Rochester, N . Y . January IO, 1923
THE PHYSICO-CHEMICAL PROPERTIES OF STRONG A N D WEAK FLOURS. 111. VISCOSITY AS A MEASURE O F HYDRATION CAPACITY AND THE RELATION OF T H E HYDROGEN ION CONCENTRATION TO IiMBIBITION I N T H E DIFFERENT ACIDS* BY ROSS
AIKEN
GORTNER AND PAUL
FRANCIS
SHARP**
In the earlier papers of this series1’?evidence was presented that strength of gluten is correlated with the colloidal condition of the wheat flour proteins. Mohs3 and later Ostwald.‘ have discussed the problems of bread making from the colloidal viewpoint. Liiers and Ostwald5 studied the viscosity of flour pastes using an Ostwald viscosimeter. The flour pastes were prepared by pouring a suspension of flour-in-water into boiling water thus gelatinizing the starch. They believe that there are two major problems in bread manufacture which should be studied from the standpoint of viscosity. The one has to do with dough formation and the other deals with dough * Presented before the Minnesota section of the American Chemical Society March, 1921, and before the Division of Physical Chemistry of t h e American Chemical Society at t h e Fall meeting, New York, N . Y . Sept. 8, 1921. Published with t h e approval of t h e Director as Paper No. 369, Journal Series, Minnesota Agricultiiral Experiment Station. Abstracted from a portion of a thesis presented by Paul F. Sharp t o the Graduate School of the IJniversity of Minnesota.in partial fulfilment of the requirements for t h e Degree of Doctor OF Philosophy, June 1922. ** From t h e Division of Agricultural Biochemistry of the University of Minnesota. R. A. Gortner and E. H . Doherty: Hydration capacity of gluten from “strong” a n d “weak” flours. Jour. Agr. Research, 13, 389-418 (1918). P. F.Sharp a n d R . A . Gortner: Physico-chemical studies of strong and weak flours. 11. The imbibitional properties of glutens from strong and weak Pours. Jour. Phys. Chem., 26, 101-138 11922). K. Mohs: Zeit. ges. Getreidew.. 7, 238-212, 250-260 (1915). W. Ostwald: Kolloid-Zeit., 25, 28-45 (1919). Liiers and W. Ostwald: Kolloid-Zeit., 2 5 , 82-90, 116-136 (1919).
